When you need to trust someone or something, there are a variety of synonyms you can use for the phrase "rely upon". Some options could include "depend on", "count on", "trust", "bank on", "repose faith in", "have confidence in", "lean on", "rest assured", "rely on", or "put one's trust in". Each of these phrases carries a slightly different connotation, with some emphasizing trust, while others emphasize the need for someone or something to be dependable or reliable. Ultimately, the right synonym to use will depend on the situation and the level of trust and confidence needed.